Finiteness, Invariance, and Analogy: A Minimal Model for Adaptive Processes
Pepijn Kroes

Abstract:
Adaptive processes are processes that adapt to the environment in which they are situated by abstracting input taken from the environment and applying those abstractions to act on the environment and to determine what next to take as input. They involve a continuous oscillation between an inductive aspect of generalization and a deductive aspect of application. This thesis proposes a minimal model for such processes in terms of three key notions: finiteness, invariance, and analogy. I take cognition to be a prototypical example of an adaptive process and examine logic from the perspective of this model. In three early traditions of logical thinking—in ancient China, ancient India, and ancient Greece—both aspects of adaptive processes can be seen to be present. Classical logic, on the other hand, focuses solely on the deductive aspect. Finally, the wider applicability and explanatory value of the model are considered, as well as other instances of adaptive processes.